The 'average' return on an investment is more nuanced than a simple mean. This calculator gives the simple average, the geometric average (also known as CAGR-equivalent), and the cumulative return - the three numbers you actually need to compare investments honestly.
Enter yearly returns in percent. Mix of positive and negative numbers is fine.
Simple average
9.57%
Arithmetic mean
Geometric (CAGR)
9.02%
Honest annualised
Cumulative
83.10%
Over 7 years
Volatility drag
Simple average is 0.55% higher than the geometric average. This gap grows when returns are volatile - it's the price of swings.
When comparing investments, use the geometric mean. It's the constant rate that produces the same end wealth as your actual return path.
These are time-weighted averages - each year's return counts equally regardless of how much you had invested. For money-weighted returns (different amounts in different years) use IRR or XIRR.
Investment returns are most commonly quoted as averages, but the 'average' you see can mean very different things mathematically - and produce wildly different decisions. A mutual fund advertising '15% average return' could be quoting the simple arithmetic mean (which overstates real performance for volatile funds) or the geometric mean / CAGR (which is honest). SEBI mandates CAGR for return claims over 1 year, but advisors and brochures sometimes blur the distinction. This calculator gives you all three numbers - simple average, geometric average and cumulative return - so you can never be misled.
The gap between simple and geometric averages is called 'volatility drag', and it's larger than most retail investors realise. A portfolio that returns +50% in year 1 and −33.3% in year 2 has a simple average return of +8.3% per year - but the geometric average is 0%, meaning ₹100 turns into ₹100 over two years. The simple-average representation is misleading; geometric is the truth. The more volatile the returns, the larger the gap. This is why direct-equity returns look more attractive on simple averages than they really are on geometric - and why disciplined index investing wins for most retail investors over long horizons.
Enter your yearly returns in percent - one row per year.
Add or remove rows as needed.
See the simple average, geometric average, and cumulative return.
Simple average is the arithmetic mean - sum the returns, divide by years. Geometric average is the constant annual rate that would produce the same cumulative return - it's always less than or equal to the simple average due to volatility drag. Cumulative return is the total compounded gain over all years.
Simple = Σ rᵢ / n ; Geometric = (Π (1 + rᵢ))^(1/n) − 1 ; Cumulative = Π (1 + rᵢ) − 1
Simple average return = sum of yearly returns / number of years. It's the arithmetic mean and is the right metric for 'expected return in any given year' - but a terrible metric for total wealth accumulation over multiple years.
Geometric average return = (product of (1 + each year's return))^(1/n) − 1. It's the constant annual rate that, compounded over the same period, would produce the actual cumulative return. Always less than or equal to the simple average; equal only if all yearly returns are identical. This is the same as CAGR - the most-quoted long-term performance metric. Always use geometric when comparing investments across different volatility profiles.
The 'cumulative return' is the total compounded return = product of (1 + each year's return) − 1. It's what your actual ₹100 grew to by the end. The geometric average is the annualised form of cumulative; the cumulative tells you the total wealth multiplier.
Fund A returns 8%, 8%, 8%, 8% over 4 years. Fund B returns 25%, -10%, 25%, -8% over 4 years. Simple average: A = 8%, B = 8%. Looks identical. Geometric: A = 8%, B = 6.91%. Cumulative: A = 36.05%, B = 30.69%. Same simple average, but Fund A delivers about ₹5,400 more on a ₹1 lakh investment over 4 years. Volatility drag is real money.
Year 1: +50%, Year 2: -33.3%. Simple average: +8.35%. Geometric: 0%. ₹100 grew to ₹150 in year 1, then dropped to ₹100 in year 2. The simple average says you earned 8.35%/year; the geometric (truth) says you earned nothing.
Always use geometric (CAGR). Simple average overstates returns for volatile investments. Two portfolios with the same simple average can have very different geometric averages - and very different real wealth at the end.
When returns are volatile, the geometric mean is lower than the arithmetic mean. A portfolio that returns +20% then −20% has a 0% simple average but a geometric average of −2.02% - you actually lose money.
Geometric average return = CAGR. Both compute the same thing - the constant annual rate that would produce the actual cumulative return.
Simple averages look better for marketing. Geometric (CAGR) is the honest number. SEBI mandates CAGR for any return claim over 1 year - but always check.
If different amounts were invested in different years, use IRR or XIRR - those are money-weighted. The averages here are time-weighted (each year's return counts equally).
Yes - when the cumulative return is negative. A fund losing money over years has a negative CAGR.
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